\documentclass{standalone}
\usepackage{tikz}
\begin{document}

\begin{tikzpicture}
\draw[step=5mm] (-3.0, -3.5) grid (3.5, 3.5);
\draw[ultra thick]
    ({2}, {3}) --
    ({3}, {2}) --
    ({2}, {2}) --
    ({2}, {-1/2+sqrt(2)}) --
    ({2+1/2*sqrt(2)}, {-1/2+1/2*sqrt(2)}) --
    ({2}, {-1/2}) --
    ({2}, {0}) --
    ({1}, {-1}) --
    ({1+1/2*sqrt(2)}, {-1-1/2*sqrt(2)}) --
    ({1}, {-1-sqrt(2)}) --
    ({2-1/2*sqrt(2)}, {-2-1/2*sqrt(2)}) --
    ({-3/2*sqrt(2)}, {-2-1/2*sqrt(2)}) --
    ({-sqrt(2)}, {-2}) --
    ({0}, {-2}) --
    ({0}, {0}) --
    ({2}, {2}) -- cycle;
\fill[red] (0,0) circle (3pt);
\end{tikzpicture}

\end{document}